Starting with the gradient based algorithms, we implemented \(\mathrm {OMD}_\mathrm {NE}\)  with the projection defined in Algorithm REF . We implemented \(\mathrm {OGD}\)  using two implementations of the projection algorithm, one by Paschos et al. [1]} for the setting \(\frac{R}{h} = 1\) , and one by Wang and Lu [2]} for the general setting \(\frac{R}{h} \ne 1\) .
